Holomorphic embedding method based Three-Phase power flow algorithm considering the sensitivity of the initial value

•A HEM based three-phase power flow model particularly for T&D systems is proposed.•Based on the matrix normal form transformation, a three-phase power flow matrix calculation structure, as well as its compact form of linear recursive equations, is constructed, with which different types of buses and grounding/ungrounded areas can be included.•The convergence principle of the proposed algorithm in solving the power flow problem to a physically meaningful solution is theoretically analyzed and verified with cases. The transmission network is generally considered as three-phase balanced, while the consideration of three-phase unbalance is mainly on distribution networks. However, with the increasingly interconnection of renewable energy, such as wind energy, onto transmission networks, non-adoption of commutation long transmission lines usually results in unbalanced line parameters. Therefore, developing reliable three-phase power flow algorithms for transmission and distribution (T&D) systems becomes more and more important for the reliable and safe operation of emerging power systems. Among the many three-phase power flow algorithms, Newton Raphson method (NRM) and its variants occupy a large share, due to their ability in dealing with multiple sources and looped sub-networks. However, they are sensitive to the initial value, and can hardly ensure convergence to a physically meaningful solution with improper initial values, especially for three-phase unbalanced system. To this end, a general three-phase power flow method for T&D systems is proposed based on the holomorphic embedding method (HEM), and the advantages of the proposed method compared with traditional NRM in solving the power flow problem to a physically meaningful solution are theoretically analyzed. Based on the IEEE 33 system, the modified IEEE 123 system, and a regional power grid in China, it is verified that the proposed method has the advantages of high computational efficiency, reliable converging ability, and independence to the initial value.